Fundamental bound on entanglement generation between interacting Rydberg atoms

TL;DR

This paper derives a fundamental lower bound on the fidelity of entangling two Rydberg atoms, accounting for decay and interaction limits, and demonstrates near-optimal laser control to approach this bound.

Contribution

It provides the first analytical bound on entanglement fidelity for Rydberg atoms and shows how to nearly reach this limit with optimized laser pulses.

Findings

Derived a lower bound for entanglement fidelity involving decay and interaction strength.

Optimized laser pulses can prepare entangled states with errors close to the fundamental bound.

The bound quantifies the minimal error achievable given physical constraints.

Abstract

We analytically derive the fundamental lower bound for the preparation fidelity of a maximally-entangled (Bell) state of two atoms involving Rydberg-state interactions. This bound represents the minimum achievable error $E \geq ( 1 + \pi/2 ) \Gamma/B$ due to spontaneous decay $\Gamma$ of the Rydberg states and their finite interaction strength $B$. Using quantum optimal control methods, we identify laser pulses for preparing a maximally-entangled state of a pair of atomic qubits with an error only $1\%$ above the derived fundamental bound.